How to Make It
In a small saucepan, simmer the vinegar over moderately low heat until reduced to 1/3 cup, about 5 minutes.
In a large skillet, melt the butter in the 2 tablespoons of olive oil. Add the mushrooms and cook over high heat, turning once, until golden, about 5 minutes. Add 3 tablespoons of the reduced vinegar and cook over low heat until the mushrooms are nicely glazed and tender, about 3 minutes. Season with salt and pepper.
Light a grill or preheat the broiler. Brush the ribs with olive oil and season with salt and pepper. Grill the ribs over moderate heat, turning occasionally, until lightly charred and cooked through, 15 to 20 minutes. Brush the ribs with the remaining vinegar and grill, turning, until nicely glazed, about 5 minutes. Transfer the ribs to a platter and serve the mushrooms alongside.